Problem Set 02

Problem Set 02 - Econ 121 – Fall 2010 UC Berkeley...

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Unformatted text preview: Econ 121 – Fall 2010 UC Berkeley Professor Cristian Santesteban Problem Set 2 Due: Thursday, September 16th at the beginning of class Problem 1 You are in charge of cost control in the SF Transit Department. A consultant comes to you with the following report: Our research has shown that the cost of running a bus for each trip down is line is $30 regardless of the number of passengers it carries. Each bus can carry 50 people. At rush hour, when buses are full, the average cost per passenger is 60 cents. However, during off­peak hours, average ridership falls to 18 people and average cost soars to $1.67 per passenger. As a result, we should encourage more rush­hour business when costs are cheaper and discourage off­peak business when costs are higher. Do you follow the consultant’s advice? Discuss. Problem 2 You are an executive for Super Computer Inc. (SC), which rents out super computers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of P cents per second. SC has two types of potential customers of equal number – 10 businesses and 10 academic institutions. Each business customer has the demand function Q = 10 – P, where Q is in millions of seconds per month; each academic institution has the demand Q = 8 ‐ P. The MC to SC of additional computing is 2 cents per second, regardless of volume. a. Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What are your profits? b. Suppose you were unable to keep the two types of customers separate and charged a zero rental fee. What usage fee maximizes your profits? What are your profits? c. Suppose you set up a two‐part tariff—that is, you set one rental and one usage fee that both business and academic customers pay. What usage and rental fees would you set? What are your profits? Explain why price is not equal to marginal cost. Problem 3 Elizabeth Airlines (EA) files only one route: Chicago‐Honolulu. The demand for each flight on this route is Q = 500 – P. EA’s cost of running each flight is $30,000 plus $100 per passenger. a. What is the profit maximizing price EA will charge? How many people will be on each flight? What is EA’s profit for each flight? b. EA learns that the fixed costs per flight are in fact $41,000 instead of $30,000. Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA’s AC curve when fixed costs are $30,000 and EA’s AC curve when fixed costs are $41,000. c. Wait! EA finds out that two different types of people fly to Honolulu. Type A is business people with demand Qa = 260 – 0.4P. Type B is students whose total demand is Qb = 240 – 0.6P. The students are easy to spot, so EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight? d. What would EA’s profits be for each flight? Would the airline stay in business? Calculate the CS of each consumer group. What is the total CS? e. Before EA started price discriminating, how much consumer surplus was the Type A demand getting from air travel to Honolulu? Type B? Why did total CS decline with pricediscrimination, even though total quantity sold remained unchanged? Problem 4 If the demand for drive‐in movies is more elastic for couples than for single individuals, it will be optimal for theaters to charge one admission fee for the driver of the car and an extra fee for passengers. True or false? Explain. Problem 5 A sales tax of $1 per unit of output is placed on one firm whose product sells for $5 in a competitive industry. a) How will this tax affect the cost curves for the firm? b) What will happen to price, output, and profit? c) Will there be entry or exit? Problem 6 Your firm produces two products, the demands for which are independent. Both products are produced are zero marginal cost. You face four consumers (or groups of consumers) with the following reservations prices: Consumer A B C D Good 1 $30 $40 $60 $90 Good 2 $90 $60 $40 $30 a. Consider three alternative pricing strategies: (i) selling the goods separately; (ii) pure bundling; and (iii) mixed bundling. For each strategy, determine the optimal prices to be charged and the resulting profits. Which strategy is best? b. Now suppose that the production of each good entails a marginal cost of $35. How does this information change your answers to (a)? Why is the optimal strategy now different? Have fun and good luck! ...
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